%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : PUZ011-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Mon Jul 18 18:21:09 EDT 2022 % Result : Unsatisfiable 7.65s 7.76s % Output : Proof 7.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PUZ011-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat May 28 22:39:23 EDT 2022 % 0.13/0.34 % CPUTime : % 7.65/7.76 % SZS status Unsatisfiable % 7.65/7.76 % SZS output start Proof % 7.65/7.76 The input problem is unsatisfiable because % 7.65/7.76 % 7.65/7.76 [1] the following set of Horn clauses is unsatisfiable: % 7.65/7.76 % 7.65/7.76 ocean(atlantic) % 7.65/7.76 ocean(indian) % 7.65/7.76 borders(atlantic, brazil) % 7.65/7.76 borders(atlantic, uruguay) % 7.65/7.76 borders(atlantic, venesuela) % 7.65/7.76 borders(atlantic, zaire) % 7.65/7.76 borders(atlantic, nigeria) % 7.65/7.76 borders(atlantic, angola) % 7.65/7.76 borders(indian, india) % 7.65/7.76 borders(indian, pakistan) % 7.65/7.76 borders(indian, iran) % 7.65/7.76 borders(indian, somalia) % 7.65/7.76 borders(indian, kenya) % 7.65/7.76 borders(indian, tanzania) % 7.65/7.76 south_american(brazil) % 7.65/7.76 south_american(uruguay) % 7.65/7.76 south_american(venesuela) % 7.65/7.76 african(zaire) % 7.65/7.76 african(nigeria) % 7.65/7.76 african(angola) % 7.65/7.76 african(somalia) % 7.65/7.76 african(kenya) % 7.65/7.76 african(tanzania) % 7.65/7.76 asian(india) % 7.65/7.76 asian(pakistan) % 7.65/7.76 asian(iran) % 7.65/7.76 ocean(Ocean) & borders(Ocean, African) & african(African) & borders(Ocean, Asian) & asian(Asian) ==> \bottom % 7.65/7.76 % 7.65/7.76 This holds because % 7.65/7.76 % 7.65/7.76 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.65/7.76 % 7.65/7.76 E: % 7.65/7.76 african(angola) = true__ % 7.65/7.76 african(kenya) = true__ % 7.65/7.76 african(nigeria) = true__ % 7.65/7.76 african(somalia) = true__ % 7.65/7.76 african(tanzania) = true__ % 7.65/7.76 african(zaire) = true__ % 7.65/7.76 asian(india) = true__ % 7.65/7.76 asian(iran) = true__ % 7.65/7.76 asian(pakistan) = true__ % 7.65/7.76 borders(atlantic, angola) = true__ % 7.65/7.76 borders(atlantic, brazil) = true__ % 7.65/7.76 borders(atlantic, nigeria) = true__ % 7.65/7.76 borders(atlantic, uruguay) = true__ % 7.65/7.76 borders(atlantic, venesuela) = true__ % 7.65/7.76 borders(atlantic, zaire) = true__ % 7.65/7.76 borders(indian, india) = true__ % 7.65/7.76 borders(indian, iran) = true__ % 7.65/7.76 borders(indian, kenya) = true__ % 7.65/7.76 borders(indian, pakistan) = true__ % 7.65/7.76 borders(indian, somalia) = true__ % 7.65/7.76 borders(indian, tanzania) = true__ % 7.65/7.76 f1(true__) = false__ % 7.65/7.76 f2(true__, Ocean) = f1(ocean(Ocean)) % 7.65/7.76 f3(true__, Ocean, African) = f2(borders(Ocean, African), Ocean) % 7.65/7.76 f4(true__, African, Ocean) = f3(african(African), Ocean, African) % 7.65/7.76 f5(asian(Asian), Ocean, Asian, African) = true__ % 7.65/7.76 f5(true__, Ocean, Asian, African) = f4(borders(Ocean, Asian), African, Ocean) % 7.65/7.76 ocean(atlantic) = true__ % 7.65/7.76 ocean(indian) = true__ % 7.65/7.76 south_american(brazil) = true__ % 7.65/7.76 south_american(uruguay) = true__ % 7.65/7.76 south_american(venesuela) = true__ % 7.65/7.76 G: % 7.65/7.76 true__ = false__ % 7.65/7.76 % 7.65/7.76 This holds because % 7.65/7.76 % 7.65/7.76 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.65/7.76 % 7.65/7.76 f4(true__, African, Ocean) = f3(african(African), Ocean, African) % 7.65/7.76 african(angola) -> true__ % 7.65/7.76 african(kenya) -> true__ % 7.65/7.76 african(nigeria) -> true__ % 7.65/7.76 african(somalia) -> true__ % 7.65/7.76 african(tanzania) -> true__ % 7.65/7.76 african(zaire) -> true__ % 7.65/7.76 asian(india) -> true__ % 7.65/7.76 asian(iran) -> true__ % 7.65/7.76 asian(pakistan) -> true__ % 7.65/7.76 borders(atlantic, angola) -> true__ % 7.65/7.76 borders(atlantic, brazil) -> true__ % 7.65/7.76 borders(atlantic, nigeria) -> true__ % 7.65/7.76 borders(atlantic, uruguay) -> true__ % 7.65/7.76 borders(atlantic, venesuela) -> true__ % 7.65/7.76 borders(atlantic, zaire) -> true__ % 7.65/7.76 borders(indian, india) -> true__ % 7.65/7.76 borders(indian, iran) -> true__ % 7.65/7.76 borders(indian, kenya) -> true__ % 7.65/7.76 borders(indian, pakistan) -> true__ % 7.65/7.76 borders(indian, somalia) -> true__ % 7.65/7.76 borders(indian, tanzania) -> true__ % 7.65/7.76 f1(ocean(Ocean)) -> f2(true__, Ocean) % 7.65/7.76 f1(true__) -> false__ % 7.65/7.76 f2(borders(indian, angola), indian) -> true__ % 7.65/7.76 f2(borders(indian, nigeria), indian) -> true__ % 7.65/7.76 f2(borders(indian, zaire), indian) -> true__ % 7.65/7.76 f2(true__, atlantic) -> false__ % 7.65/7.76 f2(true__, indian) -> false__ % 7.65/7.76 f3(african(Y2), atlantic, Y2) -> f4(true__, Y2, atlantic) % 7.65/7.76 f3(true__, Ocean, African) -> f2(borders(Ocean, African), Ocean) % 7.65/7.76 f4(borders(Y1, india), Y2, Y1) -> true__ % 7.65/7.76 f4(borders(Y1, iran), Y2, Y1) -> true__ % 7.65/7.76 f4(borders(Y1, pakistan), Y2, Y1) -> true__ % 7.65/7.76 f4(true__, Y1, indian) -> true__ % 7.65/7.76 f4(true__, angola, Y1) -> f2(borders(Y1, angola), Y1) % 7.65/7.76 f4(true__, kenya, Y1) -> f2(borders(Y1, kenya), Y1) % 7.65/7.76 f4(true__, nigeria, Y1) -> f2(borders(Y1, nigeria), Y1) % 7.65/7.76 f4(true__, somalia, Y1) -> f2(borders(Y1, somalia), Y1) % 7.65/7.76 f4(true__, tanzania, Y1) -> f2(borders(Y1, tanzania), Y1) % 7.65/7.76 f4(true__, zaire, Y1) -> f2(borders(Y1, zaire), Y1) % 7.65/7.76 f5(asian(Asian), Ocean, Asian, African) -> true__ % 7.65/7.76 f5(true__, Ocean, Asian, African) -> f4(borders(Ocean, Asian), African, Ocean) % 7.65/7.76 false__ -> true__ % 7.65/7.76 ocean(atlantic) -> true__ % 7.65/7.76 ocean(indian) -> true__ % 7.65/7.76 south_american(brazil) -> true__ % 7.65/7.76 south_american(uruguay) -> true__ % 7.65/7.76 south_american(venesuela) -> true__ % 7.65/7.76 with the LPO induced by % 7.65/7.76 south_american > tanzania > zaire > uruguay > venesuela > iran > african > f5 > f1 > f4 > f3 > borders > f2 > brazil > pakistan > india > asian > indian > atlantic > kenya > somalia > ocean > angola > nigeria > false__ > true__ % 7.65/7.76 % 7.65/7.76 % SZS output end Proof % 7.65/7.76 %------------------------------------------------------------------------------